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The template for the IH45 system is any trapezium, with its non-parallel sides equal in length. Only these non-parallel sides can be shaped and this must be in the same way, as indicated by the half-arrows. The template and any tile shape formed from it have no internal symmetry, as indicated by the dog pattern.
A translation cluster is
A section of the tiling formed by this template is shown below, with a translation cluster outlined. The two basic translations are indicated by the vectors drawn from the highlighted cluster. The tiling has an axis of glide reflection and another of mirror reflection symmetry; an example of each is shown. The symmetry group of the tiling is cm.
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